1. Field of the Invention
The present invention relates to a position control apparatus including an iterative learning control circuit suitably applied to a stage unit used in exposure apparatuses or machine tools.
2. Description of the Related Art
Iterative learning control is control in which, by repeatedly performing control (a trial) for tracking the trajectory of a target to be controlled, a deviation from the target trajectory is reduced so that high-precision control can be provided. In general, in the iterative learning control, learning can be performed by using only an input applied to a target to be controlled and an output of the target. Accordingly, non-linearity that is difficult to include in a control model and a quantization error can be compensated for. It is required for a target to be controlled to have reproducibility so that the same output is obtained from the same input. In general, scanning semiconductor exposure apparatuses and industrial robots meet this condition. Accordingly, in order to further improve the control precision, the iterative learning control can be applied to these semiconductor exposure apparatuses and industrial robots. Several applications have been proposed.
In the iterative learning control, the term “learning rule” is referred to as an algorithm in which an output is obtained through a given trial and the next input is updated in accordance with the output. One of typical learning rules is a rule in which an input value is generated by multiplying the second derivative value of a deviation by a constant matrix. In addition, by using a PD compensator for a learning rule, iterative learning control can be performed without using a control target model.
Furthermore, De Roover and his colleagues obtain such a learning filter by using an H∞ control theory (Synthesis of robust multivariable iterative learning controllers with application to a wafer stage motion system, click DE ROOVER and OKKO H. BOSGRA, International Journal of Control, 2000, Vol. 73, No. 10, pp. 968-979).
Still furthermore, U.S. Pat. No. 7,181,296 B2 describes a method in which, in addition to the above-described model-based learning rule, time-frequency analysis is used so that a robustness filter is time-varied. This method reduces an effect of noise on learning, and therefore, the learning is efficiently carried out.
In iterative learning control, an optimal input is obtained by repeatedly carrying out trials. Accordingly, it takes a certain amount of time until an input for precisely tracking the target trajectory is obtained. For example, for semiconductor exposure apparatuses, the processing time (the throughput) is an important factor for their performance. Therefore, it is desirable that the amount of time required for the learning is minimized.
In order to reduce the number of trials and obtain an optimal input, information about the target to be controlled can be actively used. However, in the above-described document, the learning filter is derived from a linear time-invariant model, and therefore, the learning filter is linear time-invariant (LTI).
Accordingly, if the parameters of a model are varied during a trial, the consistency between the model and the learning filter is not ensured. As a result, the learning performance is degraded, and therefore, the number of iterative trials and learning time increase.